Understanding the Magic: Teaching Cryptography with Just the Right Amount of Mathematics

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Information about Understanding the Magic: Teaching Cryptography with Just the Right...

Published on August 8, 2008

Author: joshuarbholden

Source: slideshare.net

Description

Cryptography is a field which has recently attracted a great deal of attention from both students and teachers of mathematics and of computer science. Students of computer science see cryptography as something which is not only "cool" but may be necessary for them to know in their future careers. Many of them do not realize, however, just how much mathematics they need to know in order to understand the algorithms which lie at the heart of modern cryptography.

Understanding the Magic: Teaching Cryptography with Just the Right Amount of Mathematics Joshua Holden Rose-Hulman Institute of Technology http://www.rose-hulman.edu/~holden Joint Meetings, 9 January 2004

What am I going to show you? • Pohlig-Hellman exponentiation cipher • Fermat’s Little Theorem • Necessary ideas for RSA • One way to mix mathematics and cryptog- raphy • A neat “magic trick”? 1

What comes before? • Shift ciphers • Modular arithmetic • Multiplicative ciphers • Euclidean algorithm and multiplicative in- verses • Block ciphers (e.g. Hill cipher) • Private-key vs. public-key ciphers 2

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